1. Field of The Invention
This invention relates to a sample rate converter; such a sample rate converter may be suitable for performing sample-rate conversion between the sampling frequencies associated with digital video formats.
2. Description of the Prior Art
It is known to provide a sample rate converter based on the following theory. The sampled signal, represented as a sequence of unit impulses .delta..sub.k =.delta. (t-kT) where k is an integer and T the sampling period, modulated by the continuous signal being sampled x(t), may be shown to consist of infinitely many repetitions of the spectrum of x(t), centred on multiples of the sampling frequency (see FIG. 5, line a). It follows that, provided the Nyquist criterion has been satisfied so that the repeat spectra do not overlap, application of a suitable low-pass filter response, such as that shown in FIG. 5, line b, to this sampled signal will allow only the baseband spectrum to be passed, and the original continuous signal to be recreated. This process therefore allows the instantaneous value of this original signal to be precisely determined at any arbitrary point between samples, as is necessary when a different sampling rate is introduced due to the non-coincidence of sample times within the two sampling structures. Using the method of the convolution integral, the low-pass filter function may be applied to the sampled data. This integral, generally expressed as: ##EQU1## is shown diagramatically in FIG. 6, where in the case of the ideal low-pass response illustrated in FIG. 5, the corresponding impulse response h(t-.tau. is the sinc(x) function shown. The integral allows the reconstructed continuous signal y(t) to be produced for any arbitrary value of t by integrating the product of the sampled signal and the symmetrical time-reversed impulse response, shifted to be centred on the point t where y(t) is to be reconstructed. This integral is evaluated in the sampled case by merely summing the products of the sample values at each sample point and the corresponding value of the impulse response at the same point.
Although this would involve an infinite number of products in the example of the ideal low-pass response indicated, the same result may be approached to any necessary degree of accuracy by the use of finite length impulse response functions, this corresponding to the use of an n-tap FIR (finite impulse response) digital filter, which may be designed to exhibit an appropriate frequency response using well-known techniques. The impulse response curve is defined by the sets of amplitude values occurring at the sample points as determined by the positions of the value y(t) being reconstructed. These sets of values may be stored as coefficient values to be applied to a transversal filter. FIG. 7 illustrates a sample rate converter which is based on the above principle. In FIG. 7, 30 denotes each stage of a shift register which has n stages (n may be 32). The output of each stage 30 is fed through a digital multiplier 31 to a summer 32. Each digital multiplier 31 also receives a multiplication coefficient (which depends on the particular stage 30 and the intersampling position) from a memory device schematically designated at 33. The actual set of coefficient values applied to the multiplier 31 to construct any arbitrary new sample position are derived from tabulated values held in addressable memory devices, these tables defining the finite impulse response function. The address applied to these devices corresponds to the position of the desired new sample point relative to the, closest original sample points, this relative position being obtained from a map of the new sample points expressed in terms of the original sample pitch. The number of entries in this table obviously increases in proportion to the precision with which this intermediate point needs to be defined, and this consideration dictates the necessary number of address bits.
This method is employed in many applications and constitutes the preferred prior art method of sample-rate conversion. The method does, however, present difficulties in implementation due to the sheer complexity of the hardware when a substantial number of filter taps is required. As a general rule, the greater the number of taps in the filter, the more accurately a given response can be approximated; many applications requiring at least 32 taps to obtain acceptable interpolation accuracy. Although complex digital filter integrated circuits have been produced, these are generally limited to only two sets of pre-defined or pre-loaded coefficients, the advantage of integration only really being obtained when the memory devices can be incorporated on the filter chip. This would demand great complexity. If the number of stages is 32 (i.e. n=32), the number of intersampling positions is 1024 and the number of bits required for multiplication coefficient is, say, 12 then 32.times.1024.times.12=.OMEGA.400 k memory bits will be required for the multiplication coefficients together with 32 multipliers, possibly of 12=12 bit accuracy.